In many areas of science, especially in biotechnology, the number of high-dimensional datasets recording multiple aspects of a single phenomenon is increasing. This increase is accompanied by a fundamental need for mathematical frameworks that can compare multiple large-scale matrices with different row dimensions. In the field of biotechnology, these matrices may represent biological reality through large-scale molecular biological data such as, for example, mRNA expression measured by DNA microarray.
Recent efforts have focused on developing ways of modeling and analyzing large-scale molecular biological data through the use of the matrices and their generalizations in different types of genomic data. One of the goals of these efforts is to computationally predict mechanisms that govern the activity of DNA and RNA. For example, matrices have been used to predict global causal coordination between DNA replication origin activity and mRNA expression from mathematical modeling of DNA microarray data. The mathematical variables that is patterns uncovered in the data correlate with activities of cellular elements such as regulators or transcription factors. The operations, such as classification, rotation, or reconstruction in subspaces of these patterns, simulate experimental observation of the correlations and possibly even the causal coordination of these activities.
These types of analyses also have the potential to be extended to the study of pathological diseases to identify patterns that correlate and possibly coordinate with the diseases.